Date of Award

8-2018

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematical Sciences

Committee Member

Dr. Robert Lund, Committee Chair

Committee Member

Dr. Peter Kiessler

Committee Member

Dr. Xin Liu

Committee Member

Dr. Brian Fralix

Abstract

There has been growing interest in modeling stationary series that have discrete marginal distributions. Count series arise when describing storm numbers, accidents, wins by a sports team, disease cases, etc. The first count time series model introduced in this paper is the superpositioning methods. It have proven useful in devising stationary count time series having Poisson and binomial marginal distributions. Here, properties of this model class are established and the basic idea is developed. Specifically, we show how to construct stationary series with binomial, Poisson, and negative binomial marginal distributions; other marginal distributions are possible. A second model class for stationary count time series -- the latent Gaussian count time series model -- is also proposed. The model uses a latent Gaussian sequence and a distributional transformation to build stationary series with the desired marginal distribution. This model has proven to be quite flexible. It can have virtually any marginal distribution, including generalized Poisson and Conway-Maxwell. It is shown that the model class produces the most flexible pairwise correlation structures possible, including negatively dependent series. Model parameters are estimated via two methods: 1) a Gaussian likelihood approach (GL), and 2) a particle filtering approach (PF).

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